I have an avatar created on another grid who has an extensive inventory. I can get him into my new world, but he can't rez any objects from his inventory, just standard prims? Can this avatar be enabled to use his very useful inventory to build my new world???

If your region is configured correctly then the avatar from the other grid should be able to rezz items from its inventory inside it.

Please note that the other avatar will need to have these items in its My Suitcase folder and that the the grid it belongs to mustn't block item exportability (if it has the Export flag implemented then you need to make sure that it is enabled for the items you wish to bring over from that grid).